Vector Math
What is a vector?
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• Has magnitude and
direction
• Has a head and a
tail
• What types of
measurements are
vectors?
Magnitude of vectors
• Length of vector is
proportional to the
magnitude
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Adding Vectors
• Vectors have a direction so you need to
take that into account when adding
• A vector sum is called “resultant”
Adding vectors in same axis
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What if vectors are at angle to
each other?
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Uh oh…
2 methods:
•Graphical (tip to tail)
•Trigonometric
Tip to Tail- graphical addition
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• Put the vectors
(keeping direction
and magnitude)
together with the tip
of the first touching
the tail of the
second
• When finished, draw
a new resultant from
the tail of the 1st to
the tip of the last
Tip to tail vector addition
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• It doesn’t matter
which order you put
them in as long as
you keep tip to tail
• Try the worksheet…
Vector Subtraction
• Think about it- what
does it mean to change
the sign of a vector?
• When subtracting, you
are basically adding the
negative of the 2nd
vector
• So same magnitude,
opposite direction
• Try some…
OK, why all the focus on
angled vectors
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• We don’t live in a 1D
world where
everything happens
on the x axis
• To deal with
projectiles and
forces we need to at
least add a 2nd
dimension
Vector Components
• This is the real world (ok, only 2d, but close enough) so things happen at
angles- not just along x and y axis
• Each vector can be considered the sum of its x and y components
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Vector Components
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Resolving Vectors into
Components- Graphical
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Vector Word Problems
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• Use vector math to solve word problems
involving displacement and velocity in 2D
• BUT you need to keep quantities in
different directions separate
Vector Word Problems
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• You can solve for any variable across the river by
using information such as distance and velocity
across the river
• But you can’t use the distance or velocity
downriver or the total distance or velocity across
at the angle
Example
• An airplane with a velocity of 100km/h
encounters a headwind (blowing against
it) of 25km/h. What is the resultant
velocity of the plane?
Answer
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Example 2
• An airplane with a velocity of 100km/h
encounters a crosswind blowing at
25km/h. What is the resultant velocity?
Answer 2
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